A workpiece chucked (or clamped) in a lathing spindle unit is rotationally driven for machining. Upon standstill of the spindle unit, the chucked workpiece can additionally be machined for example with a drill or a milling cutter. In order to ensure precise workpiece machining, the workpiece must be securely retained in a predefined angular position by the spindle unit. For example, for fixing or locking the spindle shaft, a brake can be used, e.g. an expansion sleeve disposed on the spindle shaft. If the expansion sleeve expands or deforms radially outwards, the spindle shaft is secured or clamped in its position.